Add/Sub. Vectors A & B: Find Cx & Cy

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In summary, the vector C has components of Cx = 34.77 and Cy = 28.26 when calculated with the vector addition (a) C = A + B. When calculated with vector subtraction (b) C = A - B, the components are Cx = -9.61 and Cy = -0.91. The law of sines and the law of cosines can be used to solve this problem, but using the acute angles to the x-axis is preferred. However, if the angle with the y-axis is negative, it must be converted to a positive angle for accurate calculations.
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littlesohi
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Vector A has a magnitude of 12 (in some unspecified unit) and makes an angle of 27 with the x-axis, and a vector B has a length of 22 and makes an angle of 72 with the x-axis. Fnd the components of the vector C in the following:

(a) C=A+B

Cx=

Cy=

(b) C=A-B

Cx=

Cy=
 
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  • #2
you can solve it using the law of sines and the law of cosines, but i prefer solving it with components

Vx=VxA+VxB
Vy=VyA+VyBboth make acute angles to the x-axis, so don't worry, just use those angles, but if you had something like, ''it makes a -30 degree angle with the y-axis'' (meaning it is 330 degrees in the unit circle) you have to use the 330, ALWAYS THE WHOLE WAY AROUND.know you have a big resulting triangle, try to continue yourself in the operations...
 

FAQ: Add/Sub. Vectors A & B: Find Cx & Cy

What are "Add/Sub. Vectors A & B"?

"Add/Sub. Vectors A & B" refers to the process of combining or subtracting two or more vectors in a specific direction and magnitude to determine the resultant vector.

How do I find Cx and Cy?

To find Cx and Cy, you need to first determine the x and y components of vectors A and B. Then, add or subtract the x and y components separately to find the resultant x and y components of vector C. Finally, use the Pythagorean theorem to calculate the magnitude of vector C and the inverse tangent function to find its direction.

What is the significance of vector addition and subtraction?

Vector addition and subtraction are essential concepts in physics and engineering. They allow us to combine and manipulate multiple vectors to determine the overall force, velocity, or displacement of a system. This is crucial in solving real-world problems involving motion and forces.

Can I use the same method for adding and subtracting vectors in any direction?

Yes, the method for adding and subtracting vectors remains the same regardless of their direction. However, make sure to use the correct signs for the x and y components when determining the resultant vector in a specific direction.

Are there any other methods for adding and subtracting vectors?

Yes, there are alternative methods such as the parallelogram method and the head-to-tail method for adding vectors. These methods are visually intuitive and can be used for adding more than two vectors. However, the final result will always be the same as the method of adding or subtracting the x and y components separately.

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